Top 13 Best LLM For Math And Logic

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image 6 - Top 13 Best LLM For Math And Logic

In today’s digital age, large language models (LLMs) have revolutionized the way we interact with and harness the power of artificial intelligence (AI). From answering complex questions to providing insightful explanations, LLMs have become indispensable tools for various domains. When it comes to mathematics, having an LLM specifically tailored to handle mathematical concepts and problem-solving can be immensely valuable.

In this article, we delve into the world of LLMs and explore the best options available for tackling math-related queries. These advanced language models have undergone rigorous training, incorporating vast amounts of mathematical knowledge and problem-solving capabilities. By understanding their strengths, unique features, and specific applications, we aim to provide readers with insights to make informed decisions when utilizing LLMs for mathematical tasks.

Note: They are not the best for math or logic, but rather I found that they perform better at math and logic compared to other model of similar size.

Contact me if you think some other model should be on the list.



The Smaug-72B-v0.1 is a top language model that’s open-source. It’s the first model to score more than 80 on the Open LLM Leaderboard. The model is based on techniques and datasets from previous models, with some new additions. It’s useful for a wide range of tasks and powers both Smaug-34B and 72B models.

This model is a great fit for the article “Best LLM For Math And Logic”. It performs well in tasks that require mathematical and logical reasoning. Its high score shows its effectiveness. It’s a great resource for those interested in math, logic, and open-source models.


  • Model Details: The MetaMath-Mistral-7B model is a fine-tuned version of the Mistral-7B model, specifically tailored for performance on the MetaMathQA datasets. This fine-tuning process has notably enhanced its capabilities, particularly in the GSM8K performance metric, elevating it from 66.5 to 77.7. This marks a significant improvement over its base model, llama-2-7B​​.
  • Usage and Application: The model follows a structured prompting template for handling tasks. Users can insert their query question in the given template, which is designed to facilitate step-by-step reasoning and problem-solving. This structured approach aids in generating more focused and relevant responses​​.
  • Performance Metrics: In comparative studies with other models, MetaMath-Mistral-7B has shown superior performance. For instance, in the GSM8k and MATH Pass@1 tests, it scored 77.7 and 28.2 respectively, outperforming other models like LLaMA-2-70B, WizardMath-13B, and MAmmoTH-7B in these metrics​​.
  • Popularity and Reach: The model has attracted considerable attention, as indicated by the number of downloads, though the exact figure for the last month was not specified​​.


  • Fine-Tuning and Base Model: Bumblebee-7B is another fine-tuned model based on Mistral-7B. This model has been specifically adjusted using the MetaMathQA datasets, a process that likely enhances its capabilities in handling math and logic problems​​.
  • Upcoming Evaluation Metrics: While detailed results and average performance metrics are still forthcoming, Bumblebee-7B is expected to have evaluations across various benchmarks like ARC, HellaSwag, MMLU, TruthfulQA, Winogrande, and GSM8K. These evaluations will provide insights into its proficiency across different domains​​.
  • Model Size and Specifications: The model has 7.24 billion parameters, and it utilizes F16 tensor type. This size indicates its substantial capacity for processing and generating complex language and logic patterns​​.

The Wizard Math Series

Key FeaturesFit For
– Tailored for math and logic tasks– Math and logic-related instructions
– Available in 3 sizes (7B, 13B, 70B)– Different hardware capabilities
– Excel in math instructions– Superior performance on GSM8K

The Wizard Math Series is a breakthrough in LLM (Large Language Model) technology tailored for math and logic tasks. Developed by adapting Evol-Instruct and Reinforcement Learning techniques, these models excel in math-related instructions like GSM8k and MATH. The models are fine-tuned using the innovative instruction-following math training set, enhancing their performance.

Available in three sizes – 7 billion, 13 billion, and 70 billion parameters – the Wizard Math Series accommodates different hardware capabilities, making powerful language models accessible to all. Notably, the WizardMath-70B-V1.0 model demonstrates superior performance compared to closed-source LLMs like ChatGPT 3.5, Claude Instant 1, and PaLM 2 540B on GSM8K.

This advancement signifies a remarkable stride in empowering LLMs to excel in mathematical and logical reasoning tasks, showcasing the ongoing evolution in bridging the gap between language understanding and mathematical prowess.

FreeWilly2 70B

Key FeaturesFit For
– Improved reasoning capabilities– Math and logic tasks
– Based on Llama2 architecture– Enhanced logical reasoning
– Step-by-step detective reasoning– Pushing boundaries in reasoning

FreeWilly 2 is an impressive LLM AI model, based on the Llama2 architecture, consisting of approximately 70 billion parameters. It stands out from its counterparts due to its improved reasoning capabilities, a result of innovative techniques inspired by Microsoft’s orca research paper. By adopting a step-by-step detective reasoning approach, FreeWilly 2 benefits from the collective wisdom of larger models, enabling it to exhibit enhanced logical and mathematical reasoning abilities.

While FreeWilly 2’s size demands substantial GPU resources, it offers promising potential for elevating performance in the fields of math and logic. Though not explicitly designed and tested for these domains, training and official testing have shown significant improvements compared to other models of similar scale. Users seeking AI assistance for math and logic tasks will find FreeWilly 2 to be a formidable option, pushing the boundaries of reasoning within the LLM landscape.

Orca Mini v3 13B

Key FeaturesFit For
– Unique training approach– Various language-related challenges
– Distilled insights from larger models– Diverse tasks
– Usage constraints (uncensored)– Responsible usage

Orca Mini v3 13B is a remarkable LLM model that has gained popularity due to its unique training approach. Built upon the foundation of the Llama2-13b model, Orca Mini v3 showcases the potential of larger models transferring their reasoning capabilities to smaller counterparts. The model achieves this through a meticulous fine-tuning process, where the insights and reasoning of a larger model are distilled into the smaller one.

Evaluated extensively using the Language Model Evaluation Harness developed by EleutherAI, Orca Mini v3 13B has demonstrated its prowess across a diverse array of tasks. This model inherits its capabilities from the Orca Style datasets, allowing it to excel in various language-related challenges.

It’s important to note that Orca Mini v3 13B is an uncensored model, carrying the usage constraints of the original Llama-2 model. As with any advanced AI, users should be aware of its limitations and utilize it responsibly. It’s crucial to mention that this model is provided without any guarantees or warranties.


Model Size7 billion parameters
Fine-Tuning DatasetOpenOrca dataset, inspired by Microsoft Research’s Orca Paper
Training TechniquesUtilizes OpenChat packing and is trained with Axolotl
Performance Ranking#2 on the HF Leaderboard for models under 30 billion parameters at release, outperforming most 13B models
GPU AccelerationDesigned for efficient running on consumer GPUs, making it accessible to a broader user base
Competitive EdgeCompetes favorably with some 60-billion-parameter models, showcasing its strong performance capabilities

Mistral-7B-OpenOrca is a 7-billion-parameter language model that distinguishes itself through its fine-tuning approach. It leverages the OpenOrca dataset, emulating Microsoft Research’s Orca Paper dataset, and employs OpenChat packing with Axolotl training.

This model impressively ranked #2 on the HF Leaderboard for models under 30B parameters at release, outperforming most 13B models. Notably, it’s designed to run efficiently on consumer GPUs, expanding access to high-level language processing. Mistral-7B-OpenOrca even competes with some 60-billion-parameter models, highlighting its remarkable performance in the LLM landscape.

Dolphin Llama 13B

Key FeaturesFit For
– Strong reasoning capabilities– Mathematical and logical inquiries
– Prioritizes non-commercial usage– Minimized censorship
– Inspired by Microsoft research paper– Handling math and logic tasks

Dolphin Llama 13B is an Open Source Uncensored Language Model (LLM) known for its strong reasoning capabilities within the realm of math and logic. Developed based on the llama1 architecture, it prioritizes non-commercial usage and aims to minimize censorship while maximizing usability. What sets this model apart is its unique approach to reasoning, inspired by a Microsoft research paper.

Unlike most LLMs, Dolphin Llama 13B demonstrates notable improvements in handling mathematical and logical inquiries. Although not the absolute best for these tasks, it outperforms other models of comparable size in this domain. Its step-by-step detective reasoning technique allows it to leverage knowledge from larger models, granting it enhanced abilities to tackle complex math and logic-based questions.


Key FeaturesFit For
– Uncensored nature– Creative and unrestricted content
– No inherent limitations– New possibilities in AI interactions

Wizard-Vicuna-13B-Uncensored is a powerful AI model that builds upon the foundations of the wizard-vicuna-13b model. However, it has been specifically trained with a subset of the dataset, carefully removing responses that contained alignment or moralizing aspects. The objective behind this training approach is to create a WizardLM that doesn’t inherently possess alignment, allowing alignment of any sort to be added separately. For instance, reinforcement learning from human feedback (RLHF) with a LoRA (Learning from Rewarding Agents) framework can be used to incorporate alignment.

What sets Wizard-Vicuna-13B-Uncensored apart is its uncensored nature. Unlike other models, it does not have guardrails in place. This lack of guardrails allows the model to generate responses without any inherent limitations or restrictions. This uncensored capability makes it one of the best, if not the best, 13B LLM (Large Language Model) available. With its immense capacity for generating unrestricted content, this model opens up new possibilities for creative and unrestricted AI-generated interactions.

WizardLM Mega

Key FeaturesFit For
– Rigorous filtering process– Simple mathematical and programming
– Avoids refusing to respond– Problem-solving tasks

WizardLM Mega is an exceptional LLM program that showcases the culmination of advancements in AI language models. Built upon the foundations of the Llama 13B model, it has been meticulously fine-tuned using the extensive ShareGPT, WizardLM, and Wizard-Vicuna datasets. One notable feature of Wizard Mega is its rigorous filtering process, which ensures that responses lacking meaningful insights such as generic statements, e.g., “As an AI language model…” are eliminated. Moreover, the model actively avoids refusing to respond, enhancing its usability and reliability.

WizardLM Mega stands out from its counterparts by demonstrating remarkable proficiency in handling complex mathematical and programming tasks. Its versatility and robustness are evident as it consistently applies logical reasoning to problem-solving. This remarkable consistency is a testament to the extensive training and fine-tuning process that WizardLM Mega has undergone.


Key FeaturesFit For
– Generates long and coherent responses– Wide range of tasks
– Low rate of generating false info– Detailed and accurate responses
– Freedom from censorship mechanisms– Valuable tool for various apps

Nous-Hermes-13b is an advanced AI language model that has been fine-tuned on an extensive dataset of over 300,000 instructions. Developed by Nous Research in collaboration with Teknium, Karan4D, and other contributors, this model offers impressive performance comparable to GPT-3.5-turbo in a wide range of tasks.

What sets Nous-Hermes-13b apart is its ability to generate long and coherent responses, while maintaining a low rate of generating false or inaccurate information. Another notable feature is its freedom from censorship mechanisms imposed by OpenAI. The fine-tuning process was carried out on a powerful 8x a100 80GB DGX machine, utilizing a 2000 sequence length over a span of 50 hours.

During training, the model extensively relied on synthetic GPT-4 outputs. It incorporated data from various sources, including GPTeacher, general and roleplay datasets, code instruct datasets, Nous Instruct & PDACTL (unpublished), CodeAlpaca, Evol_Instruct Uncensored, GPT4-LLM, Unnatural Instructions, as well as biology, physics, chemistry, math datasets from Camel-AI and the GPT-4 Dataset from Airoboros. In total, the model was exposed to a vast amount of information from over 300,000 instructions.

Overall, Nous-Hermes-13b is a cutting-edge LLM that excels in generating detailed and accurate responses, making it a valuable tool for a variety of applications.

Robin 13B v2

Key FeaturesFit For
– Impressive ranking– Engaging and coherent conversations
– Suitable for conversational tasks– Interactive dialogues

Robin-13B v2 is an impressive LLM (Large Language Model) that has made its mark in the field. Despite being a 13B model, it has achieved remarkable performance, even surpassing some 60B models in the LLM leaderboard with an impressive ranking of sixth place.

Robin-13B v2 shines particularly in conversational tasks, demonstrating its ability to engage in meaningful and coherent conversations with users. Whether you need to discuss a wide range of topics or seek assistance in generating natural and flowing dialogues, Robin-13B v2 excels in maintaining engaging and interactive conversations.

Wizard Vicuna

Key FeaturesFit For
– No alignment or moralizing elements– Open-ended conversational experience
– Open-source community support– Customizable alignment preferences
– Uncensored nature– Responsible usage

Wizard Vicuna is an advanced AI language model, specifically the wizard-vicuna-13b variant. It has been trained on a subset of data with responses that do not contain alignment or moralizing elements. The purpose of this training approach is to develop a WizardLM that does not have alignment built-in, allowing alignment to be added separately using methods like Reinforcement Learning from Human Feedback (RLHF) or the LoRA framework.

The development of Wizard Vicuna has been made possible thanks to the contributions and support of the open-source AI/ML community. This model aims to provide a more open-ended and flexible conversational experience, free from the constraints of predefined alignment. It allows users to add their own alignment preferences or ethical considerations as needed.

It’s important to note that Wizard Vicuna, like any uncensored model, lacks guardrails or predefined limitations. Users should exercise responsibility when interacting with the model.


StableVicuna-13B is an advanced LLM (Language Model for Math) built on the foundation of the powerful Vicuna-13B v0 model. It has been fine-tuned using reinforcement learning from human feedback (RLHF) through Proximal Policy Optimization (PPO) techniques, leveraging various conversational and instructional datasets.

One notable feature of StableVicuna-13B is its ability to apply delta weights. While using the CarperAI/stable-vicuna-13b-delta weights alone is not sufficient, by incorporating the difference between LLaMA 13B and CarperAI/stable-vicuna-13b-delta weights, users can access the correct model. To streamline this conversion process, an script is provided, allowing users to automate the conversion with ease.

StableVicuna-13B’s fine-tuning is based on a combination of three datasets. The first is the OpenAssistant Conversations Dataset (OASST1), which comprises a vast collection of human-generated, human-annotated assistant-style conversations. With 161,443 messages distributed across 66,497 conversation trees, this corpus covers a diverse range of topics and is available in 35 different languages. The second dataset used is the GPT4All Prompt Generations, containing 400k prompts and their corresponding responses generated by the GPT-4 model.

While it’s important to note that StableVicuna-13B may not excel specifically in mathematical problem-solving as compared to some of the higher-ranked AI models on the list, it still offers significant improvements over other LLMs.


Manticore-13B-Chat-Pyg-Guanaco is an impressive AI model developed by the openaccess-ai-collective. With the incorporation of the Guanaco 13B qLoRa by TimDettmers, and further quantized by mindrage, this model stands out as the most performant 13B variant in existence. Its capabilities have surpassed even those of larger 30B models, making it a truly remarkable achievement in the AI landscape.

One of the notable strengths of Manticore-13B-Chat-Pyg-Guanaco lies in its verbosity, which is similar to that of the Guanaco model. However, it also showcases improved logic and reasoning abilities, setting it apart from its predecessors. This model has undergone extensive augmentation with Guanaco qLora, resulting in broad capabilities that outshine many other Wizard or Manticore models.

Manticore-13B-Chat-Pyg-Guanaco excels in in-context learning, meaning it can understand and respond to information within a given context effectively. Within its class, this AI model showcases exceptional reasoning skills, further cementing its reputation as a high-performing and reliable resource.

While Manticore-13B-Chat-Pyg-Guanaco demonstrates outstanding performance in various areas, it may have some limitations when it comes to coding-related tasks. However, its overall proficiency and adaptability make it an excellent choice for a wide range of applications, particularly in tasks that require logical thinking and contextual understanding.

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